Deep learning is commonly used to reconstruct HDR images from LDR images. LDRstack-based methods are used for single-image HDR reconstruction, generating anHDR image from a deep learning-generated LDR stack. However, current methodsgenerate the stack with predetermined exposure values (EVs), which may limitthe quality of HDR reconstruction. To address this, we propose the continuousexposure value representation (CEVR), which uses an implicit function togenerate LDR images with arbitrary EVs, including those unseen during training.Our approach generates a continuous stack with more images containing diverseEVs, significantly improving HDR reconstruction. We use a cycle trainingstrategy to supervise the model in generating continuous EV LDR images withoutcorresponding ground truths. Our CEVR model outperforms existing methods, asdemonstrated by experimental results.